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Abels, Helmut ; Garcke, Harald ; Haselböck, Jonas

Existence of weak solutions to a Cahn–Hilliard–Biot system

Abels, Helmut , Garcke, Harald und Haselböck, Jonas (2024) Existence of weak solutions to a Cahn–Hilliard–Biot system. Nonlinear Analysis: Real World Applications 81, S. 104194.

Veröffentlichungsdatum dieses Volltextes: 29 Aug 2024 06:47
Artikel
DOI zum Zitieren dieses Dokuments: 10.5283/epub.59014


Zusammenfassung

We prove existence of weak solutions to a diffuse interface model describing the flow of a fluid through a deformable porous medium consisting of two phases. The system non-linearly couples Biot’s equations for poroelasticity, including phase-field dependent material properties, with the Cahn–Hilliard equation to model the evolution of the solid, and is further augmented by a visco-elastic ...

We prove existence of weak solutions to a diffuse interface model describing the flow of a fluid through a deformable porous medium consisting of two phases. The system non-linearly couples Biot’s equations for poroelasticity, including phase-field dependent material properties, with the Cahn–Hilliard equation to model the evolution of the solid, and is further augmented by a visco-elastic regularization of Kelvin–Voigt type. To obtain this result, we approximate the problem in two steps, where first a semi-Galerkin ansatz is employed to show existence of weak solutions to regularized systems, for which later on compactness arguments allow limit passage. Notably, we also establish a maximal regularity theory for linear visco-elastic problems.



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Details

DokumentenartArtikel
Titel eines Journals oder einer ZeitschriftNonlinear Analysis: Real World Applications
Verlag:Elsevier
Band:81
Seitenbereich:S. 104194
Datum22 August 2024
InstitutionenMathematik > Prof. Dr. Helmut Abels
Mathematik > Prof. Dr. Harald Garcke
Identifikationsnummer
WertTyp
10.1016/j.nonrwa.2024.104194DOI
Klassifikation
NotationArt
35A01 35D30 35K41 74B10MSC
Stichwörter / KeywordsCahn–Hilliard equation, Biot’s equations, Poroelasticity, Existence analysis, Mixed boundary conditions, Maximal regularity
Dewey-Dezimal-Klassifikation500 Naturwissenschaften und Mathematik > 510 Mathematik
StatusVeröffentlicht
BegutachtetJa, diese Version wurde begutachtet
An der Universität Regensburg entstandenJa
URN der UB Regensburgurn:nbn:de:bvb:355-epub-590148
Dokumenten-ID59014

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